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研究生:陳威帆
研究生(外文):Wei-FanChen
論文名稱:壁面滑移或磁場影響下體積流率變化對非牛頓流體之流動特性之分析
論文名稱(外文):Characterization of Non-Newtonian Flow with Prescribed Volume Flow Rate under the Effect of either Wall-Slip or Magnetic Field
指導教授:陳朝光陳朝光引用關係賴新一
指導教授(外文):Cha`o-Kuang ChenCha`o-Kuang Chen
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:81
中文關鍵詞:非牛頓流體微流體學滑動流動非穩態流動拉普拉斯轉換
外文關鍵詞:non-Newtonian flowmicrofluidicsslip flowunsteady flowLaplace transform
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本文研究二階流體(Second-Grade Fluid)與福格特流體(Voigt fluid)在微尺度中的單向非穩態流動,流體稀薄化(rarefaction)產生的壁面滑移效應對於微間隙平板和微管內非穩態流動(unsteady)的影響。也對非微尺度的二階流體與福格特磁流體(MHD flow of Voigt fluids)的非穩態單向流,推導出在磁場的作用下,流經兩平行面時,流速分布和壓力梯度的變動情況。
文中分別分析如何應用壓力變化控制體積流率之方法,並研究六種實例: (1)梯形活塞運動(trapezoidal piston motion);(2)等加速度(constant acceleration);(3)突然被啟動之流動(impulsively started flow);(4)突然被堵住之完全發展流動(impulsively blocked fully developed flow);(5)振動流動(oscillatory flow);(6)線性加速活塞運動(linear acceleration piston motion)。並藉由拉普拉斯轉換方法(Laplace transform technique),由管內流非穩態動量方程式推導出速度(velocity)與壓力梯度(pressure gradient)關係的解析解。
分析過程我們針對活塞運動,以肯德森數 (Knudsen number) Kn代表流體稀薄化程度,所得結果以圖形表示,並與流體無滑動邊界之結果相比較。得到以下結果,對於不同體積流率下的實例,當稀薄化效應越大,管壁的滑動現象越明顯,相對地使邊界速度也增加,在管內的速度反而減小;稀薄化效應對壓力梯度值的影響,在不同的實例中則有不同的變化。

The rarefaction effect of wall-slip conditions associated with unsteady unidirectional flows of second-grade fluid and Voigt fluids passing through a microtube or parallel microgap plates are studied in this study. The velocity profile and pressure gradient of an unsteady unidirectional flows of second-grade fluids and MHD Voigt fluids moving between two parallel surfaces under magnetic field effect are solved subsequently by the Laplace transform method.
The relationship between the change of volume flow rate and the pressure variations is analyzed for six different cases including:(1) trapezoidal piston motion, (2) constant acceleration, (3) impulsively started flow, (4) impulsively blocked fully-developed flow, (5) oscillatory flow, and (6) linear acceleration piston motion. The analytical solution of the velocity and pressure gradient for the momentum equations of unsteady flow in microtube are solved by using the Laplace transform technique.
In the analysis process, we focus on the trapezoidal piston motion. The Knudsen number( Kn) is used to represent the level of rarefaction. The results are presented graphically and compared to those of the continuum under no-slip condition. From the results, we found that, the effects of wall-slip becomes significant with the increase of rarefaction. The boundary velocity also increases as the velocity of the tube decreases with the same condition. The influence of flow rarefaction on the pressure gradient is varied quite a lot for different cases.
中文摘要 I
Abstract II
誌謝 III
目 錄 IV
圖 目 錄 VII
符號說明 VIII
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 研究動機 4
1-4 論文結構 5
第二章 理論分析 7
2-1 問題描述與基本假設 7
2-2 基本解題流程 11
2-3 基本磁流體動力學導論 15
第三章 壁面滑移效應影響下體積流率變化對二階流體之微管流動特性之分析 18
3-1 前言 18
3-2 建構方程式 18
3-3 解題程序 20
3-4 範例推導 22
3-4-1 梯形活塞運動 22
3-4-2 等加速度運動 26
3-4-3 突然被啟動之流動 26
3-4-4 突然被堵住之完全發展流動 27
3-4-5 振動流動 27
3-5 梯形活塞運動計算結果與流動特性分析 28
3-6結論 38
第四章 壁面滑移效應影響下體積流率變化對福格特流體之平行微間隙板流動特性之分析 39
4-1 前言 39
4-2建構方程式 39
4-3 解題程序 40
4-4 範例推導 43
4-4-1 等加速度活塞運動 43
4-4-2 突然被啟動的流動 46
4-4-3 線性加速活塞運動 46
4-4-4 振動流動 47
4-5 結論 48
第五章 磁場影響下體積流率變化對福格特磁流體之平行板流動特性之分析 50
5-1 前言 50
5-2建構方程式 50
5-3 解題程序 52
5-4 範例推導 54
5-4-1 等加速度活塞運動 54
5-4-2 突然被啟動之流動 57
5-4-3 線性加速活塞運動 57
5-4-4 振動流動 58
5-5 結論 59
第六章 磁場影響下體積流率變化對二階流體之平行板流動特性之分析 60
6-1 前言 60
6-2建構方程式 60
6-3 解題程序 62
6-4 範例推導 64
6-4-1 等加速度活塞運動 65
6-4-2 突然被啟動的流動 67
6-4-3 線性加速活塞運動 67
6-4-4 振動流動 69
6-5 結論 70
第七章 結論與建議 71
7-1 總結 71
7-2 建議及展望 71
參考文獻 73
附錄A 微流體學概論 78
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